(CNN) -- An Arizona state lawmaker's push to end the guarantee of birthright citizenship to the U.S.-born children of illegal immigrants on Saturday set off a protest hundreds of miles away in Pacoima, a Los Angeles suburb.

More than 1,500 people in this predominantly Latino community took part in the protest, many of them chanting "Si, se puede," the Spanish version of President Obama's 2008 campaign slogan.

The protesters fear that if Arizona passes the measure, other states will follow. Arizona state Representative John Kavanagh, a Republican, has proposed that birthright citizenship, a guarantee provided by the U.S. Constitution, be taken away from children of illegal immigrants.

The guarantee, courts have ruled, was established by the 14th Amendment, which extended birthright citizenship to former slaves after the Civil War.

Other state legislatures are considering similar measures.

Kavanagh told CNN Friday, "Dispensing citizenship like a door prize is poor policy and greatly increases the costs of education, medicating and giving other benefits to the children of illegal aliens born here."